From the textbook Neuroscience. 2nd edition:
Neuropeptides are relatively large transmitter molecules composed of 3 to 36 amino acids
Individual amino acids, such as glutamate and GABA, as well as the transmitters acetylcholine, serotonin, and histamine, are much smaller than neuropeptides and have therefore come to be called small-molecule neurotransmitters
Large proteins are around 10nm, because the amino acids wrap around each other.
This means that a good estimate of the size of neurotransmitters would be from around 0.5 to 5 nanometers.